Warm-Up Write without exponents. 1) 2) 3) 4) Simplify. Express using exponents. 5)

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Presentation transcript:

Warm-Up Write without exponents. 1) 2) 3) 4) Simplify. Express using exponents. 5)

Exponents to a Power Objectives: To find a power of a power To find a power of a product or quotient

Raising a Power to a Power For any rational number a, and any whole numbers m and n,

Example 1 Simplify. Express using exponents. (5 2 ) 3 = 5 6 (4 5 ) 6 = 4 30 (x 4 ) 7 = x 28

Practice 1) (5 4 ) 3 Simplify. Express using exponents. 2) (2 2 ) 5 3) (a 6 ) 3 4) (n 4 ) 4

Example 2 Simplify. (5x) 3 = (5x)(5x)(5x) (3z) 2 = (3z)(3z) (2y 2 ) 4 = (2y 2 )(2y 2 )(2y 2 )(2y 2 ) = 125x 3 = 9z 2 = 16y 8

Practice 1) (3y) 2 Simplify. 2) (6m) 4 3) (2a 3 ) 3 4) (4x 3 ) 2

Example 3 Simplify. (4x 5 y 2 ) 3 = 4 3 x 15 y 6 (-2x 5 y 2 ) 7 = -2 7 x 35 y 14 (2y 2 ) 4 = (2y 2 )(2y 2 )(2y 2 )(2y 2 ) = 64x 15 y 6 = -128x 35 y 14 = 16y 8

Practice 1) (4y 3 ) 4 Simplify. 2) (3x 4 y 7 z 6 ) 5 3) (-7x 9 y 6 ) 2

Example 4 Simplify.